Partitioning the hypercube into smaller hypercubes
Combinatorics
2025-12-01 v3
Abstract
Denote by Q_d the d-dimensional hypercube. Addressing a recent question we estimate the number of ways the vertex set of Q_d can be partitioned into vertex disjoint smaller cubes. Among other results, we prove that the asymptotic order of this function is not much larger than the number of perfect matchings of Q_d. We also describe several new (and old) questions.
Cite
@article{arxiv.2401.00299,
title = {Partitioning the hypercube into smaller hypercubes},
author = {Noga Alon and Jozsef Balogh and Vladimir N. Potapov},
journal= {arXiv preprint arXiv:2401.00299},
year = {2025}
}
Comments
Proofs slightly shortened and referee comments addressed